Scout by Telenav seems to be well thought of, I suspect that's the best drop in replacement for Google Maps on iPhone:

http://www.scout.me/

But I'd say OSM mobile apps tend to be a bit more focused (or bitty) than Google Maps. So, for instance:

Maps.me - concentrates on offline viewing, target market seems to be tourists, but probably useful in general.

Komoot - concentrates on hiking/biking, planning routes, giving back surfaces of trails, elevation pathways, etc.

Any idea why I can't install it on my Nexus 5?

It could be you're outside the US - Telenav have only recently moved over to OpenStreetMap, from proprietary sources, and they seem to be concentrating on getting the US version working, before rolling it out elsewhere as and when. At the same time as moving to OSM, they also bought another well-thought-of app, Skobbler, and for the moment that seems to be their international version. All rather confusing, but if that applies to you, Skobbler might be worth a go.

Check out Skobbler for OSM nav outside the US. We acquired them earlier this year and they've been instrumental in enabling us to use OSM in Scout.

Maps.me is pretty good.

Thanks for the tip, I'll check it out.